The average of $3$ numbers is $22$. If the first number is $\frac{3}{8}$ of the sum of the other two numbers,what is the first number?

In an examination,the average marks were found to be $60$. The marks of $80$ candidates had to be changed from $95$ to $70$ each,and the average came down to $55$ marks. The total number of candidates who attended the examination was:

Sachin Tendulkar has a certain average for $11$ innings. In the $12^{th}$ innings he scores $120$ runs and thereby increases his average by $5$ runs. His new average is

After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

The average of two numbers is $62$. If $2$ is added to the smaller number,the ratio between the numbers becomes $1:2$. The smaller number is

There were $35$ students in a hostel. If the number of students increases by $7$,the expenses of the mess increase by $Rs. 42$ per day while the average expenditure per head decreases by $Rs. 1$. Find the original expenditure of the mess in $Rs$.